As this insignia does not depend on which piece of armor it is placed upon, the most advisable area would be the head, arms, or feet piece. This is for three reasons:

Other insignias, one example being the Survivor Insignia, receive least benefit on the head, arms, and feet. Bloodstained, on the other hand, is equally effective on all pieces of armor, thus it's better placed on the head, arms or feet so as to allow other insignias to receive greater bonuses.

Insignias that give special armor bonuses, such as the Stalwart Insignia, require that the blow hit the armor piece they're attached to in order to take effect. The head, arms, and feet are hit least regularly, and thus the Bloodstained Insignia is best placed on one of these two armor pieces so as to allow the other defensive insignias to work their full potential.

This insignia's usefulness is based on your build so it is advantageous to have an armor piece to swap out for different builds. Since head, arms, and feet pieces are the cheapest to acquire, crafting spare pieces this way is advised.